The injection molding of thin-walled tubular articles, such as the aforementioned syringe shells, generally requires an axial introduction of the flowable plastic mass into a correspondingly shaped mold cavity defined by a recess in the mold body and a coacting core. In a multiple mold designed to produce several such tubular articles simultaneously by the hot-runner technique, axial injection is inconvenient since it requires either a large mold body, with the several recesses radiating in different directions from a central injection chamber, or a number of feed channels branching out from a common chamber which have to be individually heated to maintain the fluidity of the mass. Attempts to fill the mold cavities via off-axial injection orifices have been largely unsuccessful, owing to the eccentric flow pattern which results in irregular hardening and corresponding nonuniformity in thickness and strength. Multiple molds of this type have therefore been usually limited to the manufacture of relatively shallow workpieces, e.g. as shown in U.S. Pat. No. 3,822,856.